modify wiki

wiki/concepts/Nonlinear Finite Element Analysis.md

@@ -7,7 +7,7 @@ aliases:
   - nonlinear FEA
   - incremental finite element analysis
 created: 2026-05-28
-updated: 2026-05-28
+updated: 2026-05-29
 address: c-000011
 tags:
   - concept
@@ -25,11 +25,15 @@ related:
   - "[[Nonlinear Newmark-Beta Integration]]"
   - "[[Geometric Stiffness Matrix]]"
   - "[[Dynamic Buckling Analysis]]"
+  - "[[Abaqus Analysis Procedures]]"
+  - "[[Abaqus Constitutive Integration]]"
+  - "[[Finite Element Contact Formulation]]"
 sources:
   - "[[Finite Element Procedures]]"
   - "[[A Continuum Mechanics Based Four-Node Shell]]"
   - "[[MITC Study Notes]]"
   - "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
+  - "[[Abaqus Theory Manual]]"
 ---
 
 # Nonlinear Finite Element Analysis
@@ -48,6 +52,8 @@ The MITC study notes add the algebraic bridge from nonlinear kinematics to solut
 
 The dynamic buckling thesis uses geometric nonlinearity to build the geometric stiffness terms required for buckling eigenvalue problems, then validates the resulting program against static, vibration, and dynamic buckling benchmarks.
 
+[[Abaqus Theory Manual]] adds the production-analysis view: nonlinear procedures rely on residual equations, tangent matrices, Newton or quasi-Newton corrections, automatic increments, cutbacks, material Jacobians, and changing contact constraints.
+
 ## Why It Matters
 
 Many engineering failures, large deformation behaviors, buckling events, contact interactions, and elastoplastic responses cannot be captured by a single linear solve. Nonlinear analysis adds physical realism but also adds dependence on increments, tangent quality, convergence tests, and path-following strategy.
@@ -58,6 +64,7 @@ Many engineering failures, large deformation behaviors, buckling events, contact
 - Is the tangent matrix consistent with the residual?
 - Are increments small enough to follow the equilibrium path?
 - Do convergence criteria reflect the physical quantity of interest?
+- Are material updates and contact constraints supplying a tangent that matches the active nonlinear state?
 
 ## Sources
 
@@ -65,3 +72,4 @@ Many engineering failures, large deformation behaviors, buckling events, contact
 - [[A Continuum Mechanics Based Four-Node Shell]]
 - [[MITC Study Notes]]
 - [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]
+- [[Abaqus Theory Manual]]